Ah! an optimization problem, I love those:
Given:
400=4y+3x--------Probably x,y>0 are the other conditions
Maximize:
2xy

Since
400=4y+3x
we have by solving for y:
100-.75x=y
Thus, 2xy becomes:
2x(100-.75x) same as 200x-1.5x^2
Now maximize that function by taking the derivative:
200-3x=0
Thus,
x=200/3
Then,
100-(3/4)(200/3)=y
Thus,
100-50=y
Thus, the solution is
x=200/3 and y=50